Question for best strategy, practice question

GRE Quant Problem Solving
1

Question:

In a basket, there are a certain number of oranges and 3
3 apples. The probability of pulling two oranges out without replacement is 6 /11. What is the total number of pieces of fruit in the basket before any are removed?

My Question:

I am struggling to efficiently choose numbers to get to a quick answer here. It would be nice if sme could help me how they answered this in a timely manner.

More concretly:
In the solution video to this question at minute 1:30, you say right hand side is bigger then the left hand side and therfore implies that “x is too small”. Where does this implication come from? Could you further explain the logic behind this systematic “Choosing numbers”?

2

You don’t want to solve this algebraically?

3

The algebra gets really messy quite fast. In the solution video they also say the best way is not using algebra. But I do not quite understand how they make the “educated guesses” or when you should higher or lower when the eqn does not hold.